An airplane ascends 450 feet at a constant rate as it flies a horizontal distance of 1,000 feet. How much altitude will it gain as it flies a horizontal distance of 1 mile? (Hint: 5,280 feet = 1 mile.)
450/1000 = x/5280
multiply both sides by 5280
x = (5280) (450/1000)
To find out how much altitude the airplane will gain as it flies a horizontal distance of 1 mile, we'll need to use proportions and ratios.
Step 1: Find the altitude gained per horizontal distance for the given flight.
We are given that the airplane ascends 450 feet as it flies a horizontal distance of 1,000 feet. So, the altitude gained for 1,000 feet of horizontal distance is 450 feet.
Step 2: Convert the horizontal distance from feet to miles.
We are given the hint that 5,280 feet is equal to 1 mile. Therefore, to convert 1,000 feet to miles, we divide by 5,280:
1,000 feet / 5,280 feet/mile = 0.1894 miles
Step 3: Calculate the altitude gained for 1 mile using the ratio from step 1.
Since we know the altitude gained for 1,000 feet is 450 feet, we can set up a ratio:
1,000 feet : 450 feet = 0.1894 miles : x
Solving for x (the altitude gained for 1 mile):
x = (450 feet * 0.1894 miles) / 1,000 feet
x = 0.0854 miles
Therefore, the airplane will gain an altitude of approximately 0.0854 miles as it flies a horizontal distance of 1 mile.